What kind of written warranty did your daughter get or indeed verbally told anything. I know in S Ireland I always get a two page receipt from the SIMI dealerships Iv used.
Bought a second hand car late last year and two weeks ago developed a terrible "squeal" in the handbrake, brought it into them and even though wasnt "technically" covered they did it free of charge.
We always push for new tyres, if they not all ready on car (as well as car mats and the likes!). Tyres, to my limited knowledge are wear and tear so your own responsibility.